Properties of a Rectangle

A line $l$ is parallel to line $m$ and a transversal $p$ intersects them at $\mathrm{X},\mathrm{Y}$ respectively. Bisectors of interior angles at $\mathrm{X}$ and $\mathrm{Y}$ intersent at $\mathrm{P}$ and $\mathrm{Q}$. Is $\mathrm{PXQY}$ a rectangle ? Give reason.

The diagonals of a rectangle $\mathrm{ABCD}$ meet at point $\mathrm{O}$. If $\angle \mathrm{BOC}=44°$, find $\angle \mathrm{OAD}$.

$\mathrm{PQRS}$ is a rectangle. Diagonals $\mathrm{PR}$ and $\mathrm{QS}$ meet at point $\mathrm{O}$. If $\mathrm{OP}=2\mathrm{x}+4,\mathrm{OS}=3\mathrm{x}+1$, find $x$ and $\mathrm{QS}$

Name the quadrilaterals whose diagonals:

Are equal

The sides of a rectangle are in the ratio $4:5$. If the perimeter of the rectangle is $90 \mathrm{cm}$, find its sides.

$\mathrm{ABCD}$ is a square. Find $x$.

In a rectangle $\mathrm{KITE}$, diagonal $\mathrm{KT}=13 \mathrm{cm}$, $\mathrm{IT}=5 \mathrm{cm}$. Find $\mathrm{KI}, \mathrm{KE}$ and $\mathrm{ET}$.

In a rectangle $\mathrm{CALM}$, $\mathrm{CA}=4 \mathrm{cm}$ and $\mathrm{AL}=3 \mathrm{cm}$. Find the length of the diagonals $\mathrm{CL}$ and $\mathrm{AM}$.

$\mathrm{PACE}$ is a rectangle. Give reasons for the following:

$\angle \mathrm{POA}=\angle \mathrm{COE}$

$\mathrm{PACE}$ is a rectangle. Give reasons for the following:

$\mathrm{OA}=\mathrm{OE}=\mathrm{PO}=\mathrm{OC}$

$\mathrm{PACE}$ is a rectangle. Give reasons for the following:

$\angle \mathrm{APC}=\angle \mathrm{CEA}$